Vector boson fusion tagging with

graph neural networks

Study of the Stability of Tagging Algorithms Applied to the

Analysis of Higgs-to-Invisible Decays

Internship report

Summer Student Project - STAG-F017

Supervised by Andrea Malara and Santeri Laurila

Antoine Dierckx

ULB, Belgium

Summer 2024

Contents

1 Overview of the internship 1

1.1 Presentation of CERN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Particle accelerators at CERN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 The CMS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 The CMS collaboration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 Work environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Vector Boson Fusion and invisible decay of the Higgs 10

2.1 Higgs physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.1 Higgs production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Higgs decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Overview of the internship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Internship Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.1 Useful concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3.2 Classiﬁcation with graph neural networks . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1 PFCs cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.2 ROC curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4.3 Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5.1 Energy and transverse momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5.2 Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5.3 Eta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Conclusion 26

References 27

Abstract

The goal of this internship is to explore the feasibility of using new methods based on Graph Neural

Network (GNN) to distinguish between two production modes of the Higgs boson.

Traditionally, production modes classiﬁcation (for instance, the Higgs boson) uses high-level kine-

matic variables like the energy or the angle between particle jets. However, these variables are derived

from a more fundamental set of low-level data (for instance, the energy or the (η, ϕ) coordinate of

individual particles).

GNNs can directly process low-level data, therefore maximizing the information used, by treating the

particles as nodes in a graph.

Our main objectives are:

1. Compare the eﬃciency between GNNs and traditional variables for Higgs boson production mode

classiﬁcation.

2. Study the sensitivity of the GNNs to changes in the simulations.

3. Understand and quantify the variations of both high and low-level variables under the changes in

the simulations.

To do so, we will study samples from simulations to understand how much they change under

variations of the generators and the tunes of the latter, and how the GNN responds to these changes.

We want to quantify the impact of such variations on the physical variables as well as on the GNN

output, and on the classiﬁcation performance associated.

We show that the GNN output ﬂuctuates within 10 ∼ 20 %, while its classiﬁcation performance

remain stable within 1 %.

Cover and end illustration by Mette Ilene Holmriis.

“The curiosity of the human mind is essential if you want citizens who think rather than accept the ﬁrst

nonsense they come to.”

François Englert[1]

1 Overview of the i nternship

This internship took place at CERN in Geneva, Switzerland, as part of the STAG-F-017 course, ﬁguring the program

of Master in Physics - research-oriented. It ran from July 1 to August 2 on a part-time basis, then from August 2

to August 31 on a full-time basis.

CERN Summer Student Program

This internship echoes the structure of the CERN Summer Student Program.

The program was launched in 1962[2, 3] under the impetus of then General Manager Victor Weisskopf . It is made

in two parts: the lectures and the internship.

The lectures cover all the main aspects of physics at CERN, with 26 diﬀerent topics addressed within only ﬁve

weeks.[4] They are part of four main branches: particle physics, computing, accelerators, and statistics. The lectures

take place in the main auditorium, every morning of July. They oﬀer an opportunity to meet the other students

while the internship typically is an individual project (with the supervisor) or is conducted in small groups.

Figure 1: Lectures program for the CERN Summer Student Program 2024 [2]

The CERN Summer Student program gathers around 300 students (from member and non-member states)

pursuing bachelor’s or master’s degrees in physics, computing, engineering and math. Students come for between

8 to 13 weeks. At the end of their stay, the students are invited to present their internship in the Student Session,

where they have 10 minutes to summarize their internship.

1.1 Presentation of CERN

CERN is an international particle physics laboratory. Its acronym stands for European Organization for Nuclear

Research (Conseil Européen pour la Recherche Nucléaire) and was founded in 1952 by 12 European countries[5]. It

has 23 member states and 11 associate member states.

CERN is also an oﬃcial United Nations General Assembly observer[6]. The CERN convention, signed in 1953,

speciﬁes:

The Organization shall have no concern with work for military requirements and the results of its experimental

and theoretical work shall be published or otherwise made generally available.

In 1954, the construction began close to Geneva with the construction of the ﬁrst buildings and the Proton

Synchrotron, and the convention was ratiﬁed by the 12 founding countries, including Belgium.

Figure 2: Aerial view of the site, June 15th, 1955[7]

Figure 3: Plan of the site from Dr. Steiger, the chief

architect, and his collaborators. [7]

During the Cold War, CERN was one of the few places in the world where Western and Eastern scientists worked

side by side[8].

Today, CERN is the world’s largest particle physics laboratory, with over a billion euros budget and more than 100

nationalities. Many people are working at CERN, including[9]:

• ∼ 2 700 staﬀ

• ∼ 12 000 scientiﬁc users from ∼ 70 countries, including 129 from Belgium.

• ∼ 800 fellows

• ∼ 400 students

• ∼ 300 summer students

• ∼ 3000 contractors

The people working at CERN are either employed (MPE) or Associated (MPA). Staﬀ members and Fellows consti-

tute the MPE, while International collaboration (MPAc; users and other associates), exchange of scientists (MPAx),

and training (MPAt; students, trainees, apprentices) constitute the MPA. The vast majority of the members of

personnel are Users (∼ 70%).

The current Director General is Fabiola Gianotti.

Objectives

The main goal of CERN is to test our current understanding of particle physics and to explore physics beyond the

Standard Model. More precisely, the near-future objectives are: [10, 11]

1. “Deliver world-class scientiﬁc results and knowledge”:

• Fully exploit the potential of the Large Hadron Collider during its third and ﬁnal run, including for the

High-luminosity LHC (HL-LHC) project (new of the dipoles and quadrupoles, detector updates of Atlas

and CMS, . . . ).

• Upgrade the injector complex to allow new possibilities for experiments like ISOLDE and AWAKE.

• Support the development of neutrino physics by collaborating with the DUNE experiment in constructing

a second cryostat.

• Continue to support the theoretical particle physics.

2. Study the options for a future collider:

Study the technical and ﬁnancial feasibility of diﬀerent types of collider, including:

• The Future Circular Collider (FCC).

• The Compact Linear Collider (CLIC).

• Muon colliders.

3. Increase the return to the Member and Associate Member States, including with the industry.

4. Strengthen CERN’s impact on society

Budget

According to the CERN annual report of 2023[9], their total expenses are 1 305,6 MCHF (about the same in euros).

The repartition of the budget is illustrated in Figure 4.

In the previous years, the budget was stable: 1224.9 MCHF in 2022[12], 1228.4 MCHF in 2021[13], 1157.4 MCHF

in 2020[14] and 1259.7 MCHF in 2019[15].

Figure 4: CERN expenses [9]

The Compact Muon Solenoid program alone represent 13 070 kCHF for 2024, separated in 8340 kCHF for staﬀ

expenses and 4730 for material expenses[16]. It is a 16% decrease from last year[17].

Each Member State must contribute to CERN funding according to its GDP, in a way decided by the CERN

Council

. In 2024[18], Belgium contributed for ∼ 2, 8 % of the Member States’ contributions with around 34

million euros. Some Associate Member States also contributed ∼ 40 million euros, while the total Member States’

contribution is around 1 220 million euros.

Diversity & Inclusion Program

Promotion of diversity and inclusion at CERN dates back to the 90s[19]. In 1993, an advisory group published

recommendations for equal opportunities for women. The role of Equal Opportunities Oﬃcer (EOO) was established

in 1996, followed by the creation of the Equal Opportunities Advisory Panel (EOAP) in 1998.

By 2010-2011, a broader Diversity Program was created, and the EOO and EOAP were dissolved.

The CERN Council is the supreme decision-making authority of the Organization, composed by delegates of all its twenty-

three Member States.

Figure 5: Proportion of Female Members of the Personnel over the last 10 Years (2014 – 2023)[20]

Today, there is still a huge amount of progress to be made, even if approaches promoting inclusiveness and

diversity are increasingly present (for example, with the “25 by ’25” project).

Student Opportunities

Besides the Summer Student Program, CERN oﬀers many possibilities to pursue a career for diﬀerent types of

proﬁles and qualiﬁcations. I’ll limit myself here to opportunities for PhD students. There are three main ways of

joining CERN for a PhD:[21, 22]

1. The Doctoral Student Program:

For interests in Applied Physics, Engineering, or Computing, one can apply to this program to spend up to 36

months at CERN. Candidates must be from a CERN Member or Associate Member State. CERN provides a

contract, monthly allowance, travel support, and health insurance.

CERN typically selects around 40-50 doctoral students at each selection committee. The last one was in

February 2024.

2. The Marie-Curie PhD Position:

This program is funded by the European Union. Candidates must have a master’s degree. This program

oﬀers similar conditions that the Doctoral Student Program, with a shorter period (6 months).

3. CERN Collaboration with a university:

Any university or Institute (for example the Inter-University Institute For High Energies IIHE) collaborating

with CERN might oﬀer PhD positions on subjects closely related to the research at CERN.

In general, this means spending a few weeks to a few months a year on site (at CERN), and the rest of the

time at the university or institute.

1.2 Particle accelerators at CERN

The accelerator complex at CERN is a succession of particle accelerators with increasingly high energies. Each

machine injects the beam into the next one, the LHC being the last one.

The biggest and most powerful particle accelerator is currently the LHC (Large Hadron Collider) where particle

beams are accelerated to a peak energy of 6,5 TeV. The LHC is a 27-kilometer ring of superconducting magnets,

which bend the trajectory of the proton beams, along with several accelerating structures that boost the protons to

speeds approaching the speed of light.

Within the accelerator, two high-energy particle beams travel in opposite directions and cross each other at 4 loca-

tions. Those beams move in two tubes maintained in a vacuum. They are guided around the accelerator ring by a

magnetic ﬁeld generated by superconducting electromagnets. To keep these electromagnets in a superconducting

state, the required temperature is around −271.3 C , a temperature lower than that of outer space.

Additionally, many of the intermediate accelerators have their own experimental facilities, enabling research at

lower energy scales.

This opportunity was part of an EU project (INTENSE) for the year 2022.

Figure 6: The CERN accelerator complex layout in 2022[23]

The process of accelerating protons through CERN’s accelerator complex is as follows:

1. Before 2020, the source of the proton beam was hydrogen atoms taken from a simple bottle containing

hydrogen. The atoms were ionized, and only the protons were kept.

Since 2020, the Linear accelerator 4 (Linac4 ) is the source of proton for the accelerator complex. It accelerates

the negative hydrogen ions to 160 MeV.[24]

2. From Linac4, the beam goes to the Proton Synchrotron Booster (PSB), where the ions are stripped of their

electrons, leaving only protons. The PSB accelerates the protons to 2 GeV, after which they are transferred

to the Proton Synchrotron (PS), where they are further accelerated to 26 GeV.

3. The beam is then sent to the Super Proton Synchrotron (SPS), where the protons reach 450 GeV.

4. Finally, the protons are transferred into the LHC, where they are injected into two beam pipes, one circulating

clockwise and the other anticlockwise.

It takes 4 minutes and 20 seconds to ﬁll each ring of the LHC, and 20 minutes to accelerate the protons to

their maximum energy of 6.5 TeV. Under normal conditions, these beams can circulate for many hours.

In addition to protons, the LHC also accelerates lead ions. These ions are produced by vaporizing a puriﬁed

lead sample and injecting it into Linac3. The lead ions are collected and pre-accelerated in the Low Energy Ion Ring

(LEIR) before following the same route as protons through the PS, SPS, and LHC. The lead ions ultimately reach

a maximum energy of 2,76 TeV per nucleon in the LHC.

The products of these collisions are recorded by the ALICE, ATLAS, CMS, LHCb, LHCf, MoEDAL, TOTEM

experiments, FASER and SND@LHC.

This year is the third year of the RUN 3 of the LHC, which operates at an energy of 13.6 TeV.

1.3 The CMS detector

As Belgium is one of the institutes involved in the CMS collaboration, my internship is part of this. Therefore, I will

be focusing on the CMS experience and the associated collaboration.

Overview

The CMS detector is one of the two large detectors at the LHC (the other one being ATLAS). CMS stands for

Compact Muon Solenoid. The CMS detector is one of the largest detectors globally, measuring 21 meters in length,

15 meters in diameter, and weighing 14,000 tonnes.

The detector

The CMS detector aims to reconstruct the type of particles, their position, energy, and momentum from collisions

at the LHC. CMS has a cylindrical geometry, layered around the collision point. This cylinder is blocked on either

side by ‘’caps‘’. This particular geometry means that we have to work with an adapted coordinate system.

Figure 7: Sectional view of the CMS detector. [25].

The following coordinate system is adopted:

• We take the z axis to be the axis of the beam. At the same time, we deﬁne the plane perpendicular to

this axis, the transverse plane. Subsequently, we will consider certain quantities restricted to this plane, for

example, the transverse momentum p

, which CMS measures.

• The angle θ is deﬁned as the polar angle with respect to the z axis.

• The ϕ angle is deﬁned as the azimuthal angle, included in the transverse plane.

Deﬁnition 1.1 (Pseudorapidity). The pseudorapidity η, a function of θ, is deﬁned as follows:

η ≡ −ln



tan





] (1.1)

Property 1.1. The diﬀerences in pseudorapidity are Lorentz invariants for boosts along the z axis.

From ϕ, η and p

, one can reconstruct the three components of the momentum (p

, p

= p

cos ϕ (1.2)

= p

sin ϕ (1.3)

= p

sinh η (1.4)

(1.5)

1.4 The CMS collaboration

The CMS collaboration gathers 6288 people [26, 27] from 57 countries and regions.

“The CMS Management Board, chaired by the CMS Spokesperson, is responsible for directing the CMS experiment

following the policies agreed by the CMS Collaboration Board. The Spokesperson represents the Collaboration in

dealing with other organizations and committees, while the CMS Collaboration Board is the governing body of the

experiment that makes all major decisions.”[28, 29]

To participate in the collaboration, they are three types of membership[30]:

1. Full Membership:

The full membership includes full rights and obligations, including the right to vote in the Collaboration

Board, the ability to sign all CMS publications, and eligibility for leadership roles. Financial and operational

contributions are expected.

2. Cooperating Institute:

This type of membership concerns institutions aiming for full membership, and is limited to about ﬁve years.

Members contribute to speciﬁc projects, sign relevant publications, and participate in Collaboration Board

discussions without voting rights.

3. Associated Institute:

An associated institute would focus on technical contributions in areas like engineering or computing, without

involvement in physics analyses or ﬁnancial obligations.

Figure 8: CMS Management Board Organigram[31]

The CMS collaboration is organized in diﬀerent Coordination Areas, each specialized in some aspect of the

detector.

The diﬀerent Coordination Areas are:

Oﬄine Software and Computing (O&C), Physics Coordination (PC ), Physics and Performance Datasets (PPD),

Run Coordination (RC ), Technical Coordination (TC ), Trigger-HLT (TSG), Upgrades (UC ).

Within the Physics Coordination, there are two types of working groups: the Physics Object Groups (POGs)

and Physics Analysis Groups (PAGS)[32]. For each group, a Twiki page is available to access any useful information

and to make collaboration between groups easier.

The diﬀerent Physics Object Groups are:

BTV: B-tagging and Vertexing, TRK (Tracking), EGM (Electron and Photons), JME (Jet and Missing Energy),

MUO (Muons), TAU (Taus), LUM (Luminosity), PRO (Protons (in PPS)).

The diﬀerent Physics Analysis Groups are:

BPH (B Physics and Quarkonia), SMP (Standard Model Physics), TOP (Top Physics), HIG (Higgs Physics), SUS

(Searches for new physics in ﬁnal states with Unbalanced pT and Standard objects), EXO (Searches for Exotica),

B2G (Searches for Beyond SM particles decaying to top quarks and Higgs and Gauge bosons), HIN (Heavy-Ion

Physics).

Some tasks being useful for diﬀerent Coordination Area, a third type of groups, the Shared Groups, is consti-

tuted. The diﬀerent Shared Groups are:

Generator and MC production (shared with O&C), Machine Learning (shared with O&C), Particle Flow (shared

with PPD).

The analysis in which this internship is taking place is part of the physical coordination within the HIG group.

1.5 Work environment

I worked in a shared oﬃce with my supervisor, Dr. Andrea Malara. The oﬃce is located in the Belgian section of

building 40, on the Meyrin site. Being close to my supervisor facilitated the interactions and allowed me to ask

(many) questions when needed. The oﬃce is equipped with multiple whiteboards, which are used both for personal

use and to explain various concepts.

Next to the oﬃce is the main restaurant, R1, which is open throughout the day. It is an important place because

coﬀee breaks allow us to connect with other researchers and network for future projects.

During my internship, I worked alongside another summer student who initially focused on a similar subject. In

the ﬁrst two weeks, we followed the same introduction to coding, allowing us to assist one another. However, our

projects quickly diverged and we began to work individually.

Part of the internship is to participate in regular meetings with members of the same working group. These

meetings, typically held weekly, often included participants from diﬀerent universities, such as collaborators from

Boston and the Université Libre de Bruxelles (ULB). The main purpose of such meetings is to present updates

on ongoing research and get feedback and comments to help plan the next steps of the work. Throughout my

internship, I made 4 presentations that allowed me to work on my communication skills.

2 Vector Boson Fusion and invisible decay of the Higgs

2.1 Higgs physics

The Higgs boson is part of the Standard Model of Particles. It was discovered for the ﬁrst time at CERN in 2012,

in CMS and ATLAS.

In ATLAS, it was discovered through the h → γγ (at loop level) and the h → 4l channel. In CMS, it was discovered

through the h → 4l channel.

Since then, Higgs physics has been used to probe the Standard Model and to explore the physics beyond it.

three generations of matter

(fermions)

I II III

three generations of antimatter

(antifermions)

I II III

interactions / forces

(bosons)

mass

charge

spin

≃ 2.2 MeV

charm

≃ 1.3 GeV

top

≃ 173 GeV

down

≃ 4.7 MeV

−1

strange

≃ 96 MeV

−1

bottom

≃ 4.2 GeV

−1

QUARKS

antiup

≃ 2.2 MeV

−2

anticharm

≃ 1.3 GeV

−2

antitop

≃ 173 GeV

−2

antidown

≃ 4.7 MeV

antistrange

≃ 96 MeV

antibottom

≃ 4.2 GeV

−

electron

≃ 0.511 MeV

−1

−

muon

≃ 106 MeV

−1

−

tau

≃ 1.777 GeV

−1

electron

neutrino

< 1.0 eV

muon

neutrino

< 0.17 eV

tau

neutrino

< 18.2 MeV

LEPTONS

positron

≃ 0.511 MeV

antimuon

≃ 106 MeV

antitau

≃ 1.777 GeV

electron

antineutrino

< 1.0 eV

muon

antineutrino

< 0.17 eV

tau

antineutrino

< 18.2 MeV

gluon

photon

Z boson

≃ 91.2 GeV

−

W boson

≃ 80.4 GeV

−1

W boson

≃ 80.4 GeV

GAUGE BOSONS

VECTOR BOSONS

Higgs

≃ 125 GeV

SCALAR BOSONS

Figure 9: Summary of the elementary particles of the Standard Model [33]

2.1.1 Higgs production

The Higgs production depends on the characteristics of the accelerator: what is being collided (proton-proton,

electron-electron, heavy ions, etc.), what is the energy in the center of mass, . . .

Figure 10: Feynman diagram associated to the

ggH production mode

Z or W

∓

Figure 11: Feynman diagram associated to the

VBF production mode

ggF

At the LHC, the main production mode is the gluon-gluon fusion (ggF ): the emission of two gluons from the protons,

that go into a quark loop (dominated by the contribution of the top quark

) and produce a Higgs boson.

It’s relative branching ratio at

√

s = 13 TeV is σ/σ

tot

√

≈ 87%[34].

the Higgs boson couples approximately 35 times more strongly to the top quark than to the next heaviest quark, the

bottom quark, resulting in the bottom quark’s contribution being suppressed by a factor of 35

VBF

The second most important channel is the vector boson fusion (VBF ): the emission of two vector bosons (either

two Z or a W

and a W

−

) that fuse to form a Higgs boson.

Each initial-state quark emitting a vector boson remains roughly along its initial direction, staying close to the beam.

They will hadronize and produce two forward jets in the ﬁnal state. If we denote the η coordinate of each jet η

and η

, this means that

∆η ≡ |η

− η

| > 1 (2.1)

It’s relative branching ratio at

√

s = 13 TeV is σ/σ

tot

√

≈ 7%[34].

2.1.2 Higgs decay

Unlike the Higgs production, the Higgs decay is independent of the energy in the center of mass and of the

characteristic of the accelerator.

Figure 12: Higgs branching ratios and their uncertainties for the low mass range.[35]

Background

The Higgs boson mainly decays into a bottom quark and antiquark (b

b), with a branching ratio of B

H→b

≈

58%. However, investigating this decay mode poses signiﬁcant experimental challenges. In the dominant gluon-

gluon fusion (ggF) production mode, the H → b

b signal is often overwhelmed by backgrounds generated through

quantum chromodynamics (QCD) multijet events [36].

To date, the LHC has successfully observed all the main production modes and most of the key decay channels of

the Higgs boson, including decays into b

b, W W , τ

τ, Z Z , and γγ.

Signal

One of the rarer decay channels of the Higgs boson involves its decay into invisible particles. Within the Standard

Model, the only invisible decay of the Higgs boson occurs via H → Z Z → 4ν, with a branching ratio of B

H→Z Z →4ν

≈

0.1%.

However, various theoretical models propose that the Higgs boson could act as a portal between the Standard Model

and a dark sector. In such scenarios, the Higgs boson might decay into a pair of dark matter (DM) particles, which

would not interact with the detector material, thereby contributing to the branching ratio. As a result, the direct

search for these invisible decays of the Higgs boson is a crucial approach for investigating dark matter production

and Beyond Standard Model physics.

2.2 Overview of the internship

The goal of this internship is to contribute to a better understanding of the decay of the Higgs boson into invisible

particles. We will focus on the vector fusion production (VBF ) and the Higgs to invisible decay (Hinv).

Observed and expected upper limits on (σ

VBF

/σ

) × B(H → inv) at 95% C.L. for 2012–2018 data are presented in

Figure 13. The combination of data collected in 2012, 2015, 2016, 2017, and 2018 sets an observed (resp. expected)

upper limit on the invisible decay branching ratio of the Higgs boson, B(H → inv) at less than 18% (resp. 10%)

with 95% conﬁdence. This is the most precise constraint on B(H → inv) achieved so far[37].

Figure 13: Observed and expected 95% CL upper limits on

(σ

VBF

/σ

) × B(H → inv) for all data-taking years considered,

as well as their combination, assuming an SM Higgs boson with

a mass of 125.38 GeV.[37]

Z or W

∓

Figure 14: Feynman diagram associated

with the VBF Higgs production decaying

into unknown particles χ

This summer project is part of the eﬀort of developing a Neural Network capable of distinguishing between ggF

from VBF production modes. The traditional discrimination method uses high-level kinematic variables, while the

new approach using a graph Neural Network is trained with low-level variables.

Deﬁnition 2.1. We distinguish two types of variable:

1. low-level variables: measurements provided by the detectors (ex:

→

p , E

, η, . . . for each individual particle)

2. high-level variables: non-linear combinations of low-level variables that capture useful high-level informa-

tion ( p

of reconstructed jet, number of particles in each jet, . . . )

[38]

The discrimination power of these diﬀerent methods between ggF and VBF production modes is compared using

simulated event samples.

Signature

To classify the events, we look at their signature: number of reconstructed jets, number of muons, angles between

the jets, and so on. This allows us to make selections to select particular productions and decay modes. In the

VBF-Hinv case, we expect:

• Two jets coming from the hadronization of the two quarks the emitted the vector bosons

• Large angular separation between those two jets

• Large invariant mass of the reconstructed jets

• Missing transverse energy

Deﬁnition 2.2. The invariant mass of a physical system is deﬁned as:

M b= p

− p

(2.2)

Interesting variables to discriminate the signal (VBF-Hinv) from the background (everything else) could therefore

be the diﬀerence of η between the two jets, and the invariant mass of the two jets.

Despite the cuts one could apply to the events, one can expect background from the ggH production mode. We

show a few examples of higher-order processes that could contribute to the background by mimicking the signature:

Machine Learning

Instead of using the usual variables, one could be tempted to use a combination of those (and/ or a combination

of low-level ones) in order to maximize the event tagging. A way to ﬁnd such a combination is to use machine

learning.

2.3 Internship Objectives

Since the variable generated by the Deep Neural Network is trained on simulation, one has to make sure that the

use of diﬀerent generators or tunes does not change signiﬁcantly the results of the tagging.

Let’s ﬁrst introduce some concepts in order to deﬁne precisely the goal of the analysis.

2.3.1 Useful concepts

Generators and Tunes

In particle physics, an "event" describes the outcome of a particle collision or decay process, where the ﬁnal-state

particles must conserve the energy, momentum, and quantum numbers of the initial state. Due to the random

nature of quantum processes, these events vary, with the number and properties of outgoing particles changing each

time. The probability distributions governing these variations can be inferred from experimental data or predicted

by theoretical models.

An "event generator" is a tool used to simulate these events based on the theory. These simulations are then

compared with data from the detectors. PYTHIA is one of the most widely used event generators in particle physics.

It models the complex interactions and decays that occur during collisions (see Figure 15), producing a detailed

account of the resulting particles and their properties.

Figure 15: Schematic of the structure of a pp → tt event, as modelled by PYTHIA[39]

The predictions of PYTHIA depend on some free parameters that must be tuned to match experimental data.

Thanks to the factorization theorem, the generation process can be split into several steps. Let’s list some of them:

1. Hard Scattering: Two partons from the incoming hadrons undergo a hard collision, producing outgoing

particles based on parton distribution functions and matrix elements from perturbation theory.

2. Resonance Decays: Short-lived resonances, such as W, Z bosons, or top quarks, decay into stable particles.

3. Radiative Corrections: Matrix-element corrections and parton showers account for initial and ﬁnal-state radi-

ation, adding more particles to the event.

4. Multiple Parton Interactions (MPI): Additional parton scatterings occur, adding complexity to the event,

distinct from “pileup” from multiple collisions.

5. Color Reconnection and String Formation: Partons are conﬁned into strings, which fragment into hadrons.

Color reconnection may alter the string conﬁguration before fragmentation.

6. Hadronization: The strings fragment into hadrons, which may experience Bose-Einstein or Fermi-Dirac eﬀects.

7. Hadron Decays: Unstable hadrons decay into stable particles.

8. Final-State Interactions: In densely populated regions, particles may rescatter or recombine before the event

concludes.

To generate the matrix element, the POWHEG (for Positive Weight Hardest Emission Generator) method is used.

It is designed to interface next-to-leading order (NLO) QCD calculations with parton shower simulations, to simulate

the behavior of particles after a collision more precisely.

Indeed, PYTHIA only simulates particle emissions at the leading logarithmic level, which is not accurate enough

for precise measurements. To improve the accuracy, NLO calculations need to be incorporated. When the matrix

element has been generated, PYTHIA is used for radiative corrections.

The generator’s behavior can be modiﬁed by changing its internal parameters or by applying diﬀerent models for

speciﬁc processes like parton showers. These modiﬁcations are done by tuning parameters to match the experimental

data better. To get accurate simulation of “underlying event” (everything which is not coming from the primary

hard scattering process, nor pile-up), a speciﬁc tuning of PYTHIA 8, based on the data from the CMS experiment,

is used: CP5 (standing for CMS PYTHIA 8 Tunes).

More detailed information about CP tunes can be found in the following reference: [40].

CP5 tune can be set on 3 modes: Central, Up and Down.

Weight

Weights are factors applied to individual events or processes in a Monte Carlo simulation to account for various

uncertainties or to implement corrections based on diﬀerent theoretical assumptions. Common examples include

ISR (Initial-State Radiation) and FSR (Final-State Radiation) weights, which adjust how much radiation is emitted

before or after the main scattering event. Such weights can be set on 3 modes: Central, Up and Down[41]

Unlike the generator settings or tunes, which must be conﬁgured before the simulation is run, weights can be

applied and adjusted after the events have already been generated.

Particle Flow Candidates (PFC)

A particle ﬂow candidate is the output of the particle ﬂow algorithm, which represents a stable particle, such as a

charged hadron, neutral hadron, photon, electron, or muon, as reconstructed from the detector signals.

These candidates are derived by associating and integrating data from various subsystems of the detector, including

calorimeter clusters (from ECAL and HCAL), tracks from the tracker, and hits in the muon system.

Each Particle Flow Candidate is characterized by its momentum components, energy, charge, and type, etc. Such

variables are referred as low-level variables.

The PFCs present in this analysis are: charged hadrons, neutral hadrons, photons, muons, hadrons in HF

(charged and neutral hadrons detected in the Hadronic Forward calorimeters), and electromagnetic in HF (charged

and neutral non-hadronic matter detected in the Hadronic Forward calorimeters).

2.3.2 Classiﬁcation with graph neural networks

Classiﬁer and ROC curve

As mentioned in the section 2.2, we would like to classify the events to discriminate ggF from VBF.

Such an algorithm is called a classiﬁer.

Deﬁnition 2.3. We deﬁne the True Positive Rate TPR and the False Positive Rate FPR as:

TPR ≡

TP + FN

(2.3) FPR ≡

FP + TN

(2.4)

where TP stands for True Positive and FN for False Negative.

The TPR represents the proportion of correctly identiﬁed signal events relative to the total number of true signal

events. The FPR, on the other hand, indicates the proportion of background events that are erroneously classiﬁed

as signal.

Figure 16: Illustration of the True Positive Rate and the False Positive Rate[42].

The performance of the classiﬁers is depicted using a certain type of curves. Selecting a threshold determines

classiﬁcation: events to the right of the threshold are labeled as signal, while those to the left are labeled as

background. As the threshold is varied incrementally, corresponding TPR and FPR values are obtained, which are

then plotted to generate the ROC (Receiver Operating Characteristic) curve. Hence, a ROC curve is the set of

coordinates



FPR(cut), TPR(cut)



∈ [0, 1] × [0, 1] ∀ cut ∈ R

(2.5)

The model’s classiﬁcation performance is quantiﬁed by the Area Under the Curve (AUC), which measures the

model’s ability to distinguish between classes. A higher AUC reﬂects superior model performance.

ParticleNet

ParticleNet is a type of graph neural network (GNN) architecture, based on the Dynamic Graph Convolutional Neural

Network (DGCNN).

ParticleNet originates from jet tagging, a process aimed at identifying the particles that initiate a jet. This model

treats a jet as an unordered permutation-invariant set of particles, each carrying a feature vector, much like a point

cloud. Using this technique, ParticleNet has shown signiﬁcant improvements in jet tagging accuracy compared to

previous methods.

A key component of ParticleNet is the edge convolution (EdgeConv) operation, which starts by representing a

point cloud as a graph. Each vertex corresponds to a point, and edges connect each point to its k nearest neighbors.

In this way, a local patch needed for convolution is deﬁned for each point as the k nearest neighboring points

connected to it.

Figure 17: The structure of the EdgeConv block.[43]

Figure 18: The architectures of the ParticleNet [43]

Figure 17 illustrates that EdgeConv needs two classes of features as input: the “coordinates”, which include the

relative values of η and ϕ for each PFC, and “features”



, log

), η, ϕ, energy, log

(energy), pdgId

, charge, puppiWeight



The EdgeConv block begins by identifying the k nearest neighbors for each particle, using the input coordinates to

calculate distances. The “edge features” for the EdgeConv operation are then created from the “features” input,

based on the indices of these nearest neighbors.

The EdgeConv operation uses a three-layer Multilayer Perceptron (MLP), where each layer consists of a linear trans-

formation, batch normalization, and ReLU activation. It includes a shortcut connection inspired by ResNet, allowing

input features to bypass the transformation layers.

On the other hand, ParticleNet architecture is composed of three EdgeConv blocks, where the ﬁrst block uses

particle coordinates in η − ϕ space to compute distances, and the subsequent blocks use learned feature vectors.

Each block considers 16 nearest neighbors, with increasing channel sizes across the blocks. After the EdgeConv

blocks, global average pooling aggregates the features, followed by a fully connected layer with ReLU activation and

dropout to prevent overﬁtting.

The ﬁnal output for binary classiﬁcation is produced by another fully connected layer, followed by a softmax function.

“PDG Identiﬁers are digital object identiﬁers assigned and used by PDG to reference items of PDG data such as particles,

particle properties, decay modes and review articles. ”[44]

The PileUp Per Particle Identiﬁcation weights encode the probability that each particle originates from pileup rather than

from the primary vertex.[45]

Regarding the classiﬁcation with graph neural network, the performance of the ParticleNet architecture is eval-

uated on all events. The training of the ParticleNet model was done by the collaborators in the analysis team. Its

output, the DNN score, is a number between 0 and 1 and represents the probability that the input belongs to a

particular class.

2.3.3 Objectives

Now that we introduced the various concepts, we are ready to precisely deﬁne the objectives of the analysis.

We want to quantify the impact of tunes and weights variations on high and low-level variables, as well as on

the DNN score.

1. We’ll study variations of parton shower (PS) weights (both on ggH and VBF):

ISR and FSR, ↑ and ↓

2. We’ll study pythia8 with tunes (on VBF only):

CP5 (nominal), CP5 ↑ and CP5↓

We are analyzing deviations from the nominal, focusing on signiﬁcant ﬂuctuations (beyond statistical noise),

consistent oﬀsets where results remain systematically above or below the expected values, and shape eﬀects

where deviations occur only in speciﬁc regions of the range.

Remark. We restrict the tune analysis to the signal, as samples of the CP5↑ and CP5↓ variations for ggH were not

yet available at the time of the internship.

Remark. The number of events in each sample varies a lot. Indeed, for VBF, CP5 ↑ and CP5↓ only contain ∼ 3000

events, while CP5 (nominal) has ∼ 6000 events. For ggH on the contrary, the number of events is ∼ 40000, which

lowers signiﬁcantly the ﬂuctuations due to the lack of statistics.

2.4 Analysis

To perform the analysis, we ﬁrst need to clean the Particle Flow Candidates. Then, we feed the DNN with the 100

ﬁrst PFCs (the ones with the greatest momentum). The DNN gives back the DNN score both for the signal and

the background, which allows us to plot the ROC curve associated.

2.4.1 PFCs cleaning

Final cleaning on PFCs

We impose

1. min p

= 0.2 G eV and max p

= 10 TeV and |η| < 5.2

2. p

≥ 1 G eV if the PFC is a photon

3. p

≥ 3 G eV if the PFC is a hadron in HF, an electromagnetic in HF, a neutral hadron or a muon.

4. PFC from primary vertex

Updates to the cleaning algorithm

The training of the DNN was made with a bug in the code.

Namely, the neutral mask used was of the form:

old neutral mask ≡



id = i | id = j | . . .



| p

> 3 G eV

And was not aﬀecting the muons. The new mask is of the form:

new neutral mask ≡



id = i & id = j & . . .



| p

> 3 G eV

If adding the muon to the mask did not aﬀect signiﬁcantly the

performance of the DNN, swapping the or conditions by the

and ones did.

This result is shown in Figure 19. In this ﬁgure, we used the

following labeling:

• dNN nominal for the ROC curve from the DNN output

produced with the new neutral mask, aﬀecting the muons.

This is the cleaning algorithm used in the rest of this

analysis.

• dNN_1 for the ROC curve from the DNN output pro-

duced with the old neutral mask, not aﬀecting the muons.

• dNN_2 for the ROC curve from the DNN output pro-

duced with the old neutral mask, aﬀecting the muons.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Signal (VBF)

2−

1−

Background (ggH)

(13.6 TeV)

CMS

Simulation

Work in progress

dNN nominal AUC=0.77558

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

dNN_1 nominal AUC=0.80973

dNN_2 nominal AUC=0.81013

dNN nominal AUC=0.77558

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

dNN_1 nominal AUC=0.80973

dNN_2 nominal AUC=0.81013

Figure 19: Evolution of the ROC

curve under diﬀerent PFCs cleaning

Discussion on PFC Energy Distribution

The simulation samples present a non-physical distribu-

tion of the total energy of the PFCs.

Namely, we observe events until 35 TeV , both for ggH

and VBF.

However, this must be put into perspective given the

small number of events above 14 TeV .

Remark. Naturally, the weights do not modify the maxi-

mum total energy reached by the PFCs.

4−

3−

2−

1−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

Nominal

CP5 Up

CP5 Down

Background

0 500010000150002000025000300003500040000

Total energy of the PFCands [GeV]

0.8

1.2

Ratio

Figure 20: Total energy of the PFCs, varying under

CP5 tunes

2.4.2 ROC curves

DNN score

The DNN score for ggH and VBF, under the weights and the tunes variations are:

4−

3−

2−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DNN score

0.8

0.9

1.1

1.2

Ratio

Figure 21: DNN score for ggH,

varying under PS weights

4−

3−

2−

1−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DNN score

0.8

0.9

1.1

1.2

Ratio

Figure 22: DNN score for VBF,

varying under PS weights

4−

3−

2−

1−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

Nominal

CP5 Up

CP5 Down

Background

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

DNN score

0.9

0.95

1.05

1.1

Ratio

Figure 23: DNN score for ggH

and VBF, varying under CP5

tunes

The corresponding ROC curves are:

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Signal (VBF)

2−

1−

Background (ggH)

(13.6 TeV)

CMS

Simulation

Work in progress

DNN_score nominal AUC=0.77976

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

DNN_score ps_isr_up AUC=0.78212

DNN_score ps_isr_down AUC=0.77717

DNN_score ps_fsr_up AUC=0.77478

DNN_score ps_fsr_down AUC=0.78743

DNN_score nominal AUC=0.77976

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

DNN_score ps_isr_up AUC=0.78212

DNN_score ps_isr_down AUC=0.77717

DNN_score ps_fsr_up AUC=0.77478

DNN_score ps_fsr_down AUC=0.78743

Figure 24: ROC curve of the DNN score, varying

under PS weights

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Signal (VBF)

2−

1−

Background (ggH)

(13.6 TeV)

CMS

Simulation

Work in progress

DNN_score_full_ AUC=0.77558

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

DNN_score_full_down AUC=0.78836

DNN_score_full_up AUC=0.77720

DNN_score_full_ AUC=0.77558

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

DNN_score_full_down AUC=0.78836

DNN_score_full_up AUC=0.77720

Figure 25: ROC curve of the DNN score, varying

under CP5 tunes

We observe that the DNN score can vary within ∼ 10 −20% when we vary the Parton Shower weights and the

CP5 tunes, but the ROC curves stay stable within ∼ 1%.

To track the evolution of the cut in the ROC analysis, we plotted points for ﬁxed values of the DNN score,

namely at DNN score = 0.7, DNN score = 0.8 and DNN score = 0.9. We do not see big changes among the

variations.

Remark. As expected, those tracking points are purely horizontal for the CP5 variations, since the background is

ﬁxed. To understand where the DNN score of ggH variation comes from, we need to study the low-level variable.

Before diving into the analysis, let’s show the same ROC curves for the invariant mass of the two jets.

Invariant mass of the two jets m

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Signal (VBF)

2−

1−

Background (ggH)

(13.6 TeV)

CMS

Simulation

Work in progress

SR_dijet_mass nominal AUC=0.78239

SR_dijet_mass greater than 0.7

SR_dijet_mass greater than 0.8

SR_dijet_mass greater than 0.9

SR_dijet_mass ps_isr_up AUC=0.78520

SR_dijet_mass ps_isr_down AUC=0.77927

SR_dijet_mass ps_fsr_up AUC=0.78171

SR_dijet_mass ps_fsr_down AUC=0.78301

SR_dijet_mass nominal AUC=0.78239

SR_dijet_mass greater than 0.7

SR_dijet_mass greater than 0.8

SR_dijet_mass greater than 0.9

SR_dijet_mass ps_isr_up AUC=0.78520

SR_dijet_mass ps_isr_down AUC=0.77927

SR_dijet_mass ps_fsr_up AUC=0.78171

SR_dijet_mass ps_fsr_down AUC=0.78301

Figure 26: ROC curve of the m

, varying under

PS weights

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Signal (VBF)

2−

1−

Background (ggH)

(13.6 TeV)

CMS

Simulation

Work in progress

SR_dijet_mass_full_ AUC=0.78239

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

SR_dijet_mass_full_down AUC=0.79442

SR_dijet_mass_full_up AUC=0.78193

SR_dijet_mass_full_ AUC=0.78239

DNN_score greater than 0.7

DNN_score greater than 0.8

DNN_score greater than 0.9

SR_dijet_mass_full_down AUC=0.79442

SR_dijet_mass_full_up AUC=0.78193

Figure 27: ROC curve of the m

, varying under

CP5 tunes

We see that the variable m

furnishes a better classiﬁer than the DNN score after the change in PFC selection

(higher area under the curve). We can suspect that after retraining the DNN on the new selection, the performance

of the latter would outperform the classiﬁer power of m

2.4.3 Distributions

The DNN sees only the 100 ﬁrst Particle Flow Candidates, and is given the following variables for training:

(

, log(p

), η, ϕ, energy, log(energy), pdgId, charge, puppiWeight, fromPV

)

(2.6)

We then analyze the variation of those variables, limited to the ﬁrst 100 Particle Flow Candidates. To reﬁne the

analysis, we classify the PFCs depending on their ﬂavor and with a jet-related selection.

Remark. We normalize the integral of each distribution against the integral of the nominal.

Jet related selections

The η of each PFC being known, we classify them by their position relative to the jets.

Deﬁnition 2.4. The angular distance ∆R between two objects is deﬁned by

∆R ≡

(∆η)

+ (∆ϕ)

(2.7)

The following selections are deﬁned:

1. in_jet_1:

∆R

PFC−jet

< 0.4 (2.8)

2. in_jet_2:

∆R

PFC−jet

< 0.4 (2.9)

3. in_any_jet:

in_jet_1 | in_jet_2 (2.10)

4. not_in_any_jet:

¬in_jet_1 & ¬in_jet_2 (2.11)

5. within_jets:



(η

jet

< η < η

jet

) | (η

jet

< η < η

jet

)



& not_in_any_jet (2.12)

6. outside_jets:



(η < η

jet

& η

jet

< η) | (η < η

jet

& η

jet

< η)



& not_in_any_jet (2.13)

η < η

outside jets

< η

outside jets

< η < η

within jets

Figure 28: Illustration of the two regions deﬁned by the jets

The PFCs not_in_any_jet (that includes within_jets and outside_jets) can be interpreted as coming from

underlying events.

2.5 Results

The general results are the following:

1. The signal VBF is generally much more stable than the background ggH under the change of weights,

with ﬂuctuations typically of the order of the statistical uncertainty of the nominal. Therefore, the VBF

weight variations will not be displayed in this report.

2. The parton shower weights Initial State Radiation tend to give the greatest oﬀset from the nominal, by

the order of ∼ 5 −10%. Those eﬀects virtually disappear when the distributions are normalized to a ﬁxed

value.

3. The parton shower weights Final State Radiation tents to give shape eﬀects of the order of ≲ 5%. Those

eﬀects are unaﬀected by normalization.

4. Due to the lack of statistics, results on CP5 variations are more diﬃcult to interpret. We can nevertheless

see that there is no dramatic diﬀerence between the nominal and CP5↑ and CP5↓.

5. The subregion where the greatest variations are observed is usually:

• within_jets

• restricted to charged hadrons

We can link those variations to the presence of underlying events.

2.5.1 Energy and transverse momentum

We observe ﬂuctuation at high and low p

for ggH. At low p

, the most important variations are observed for

charged hadron within_jets. The same behavior is observed for the photons, the charged hadrons in HF, and the

neutral hadrons.

At high p

, most of the events are logically coming from in_any_jet.

4−

3−

2−

1−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

0 20 40 60 80 100 120 140

[GeV]

Transverse momentum p

0.9

0.95

1.05

1.1

Ratio

Figure 29: p

of the ﬁrst 100 PFCs for ggH, vary-

ing under PS weights

4−

3−

2−

1−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

[GeV]

Transverse momentum p

0.9

1.1

Ratio

Figure 30: p

of charged hadrons (restricted to

the ﬁrst 100 PFCs) for ggH, within_jets, varying

under PS weights

The CP5 tunes variations seem to ﬂuctuate around the nominal, without clear oﬀ-set of shape eﬀect. This

behavior can be explained by considering the low number of events.

4−

3−

2−

1−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

Nominal

CP5 Up

CP5 Down

Background

0 20 40 60 80 100 120 140

[GeV]

Transverse momentum p

0.8

1.2

Ratio

Figure 31: p

of the ﬁrst 100 PFCs, varying under

CP5 tunes

4−

3−

2−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

Nominal

CP5 Up

CP5 Down

Background

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

[GeV]

Transverse momentum p

0.8

1.2

Ratio

Figure 32: p

of the ﬁrst 100 PFCs, varying under

CP5 tunes

Concerning the energy, the greatest variation appears

for charged hadrons and photons within_jets for

ggH under the PS weights variation.

The deviation is of order ∼ 5 − 10%. We observe

deviations of order ∼ 5% for the neutral hadron

within_jets too.

Under the CP5 tunes variation, we observe ﬂuctuations

around nominal that can reach up to 40 % of the sig-

nal in some subregion (for instance, charged hadrons

within_jets), but there is no clear deviation.

4−

3−

2−

1−

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

0 10 20 30 40 50 60 70

Energy [GeV]

0.9

0.95

1.05

1.1

Ratio

Figure 33: Energy of charged hadrons (restricted

to the ﬁrst 100 PFCs) for ggH, within_jets,

varying under PS weights

2.5.2 Charge

We observe a typical variation of order ∼ 5% for the

ggH under PS weights variation.

The subregion where the variation is the most impor-

tant is within_jets. Similar behavior is found for

charged hadrons, neutral hadrons, and photons.

The ﬂuctuations for VBF under CP5 tunes variations

are less important, of order of ≲ 5%.

0.1

0.2

0.3

0.4

0.5

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

1.5− 1− 0.5− 0 0.5 1 1.5

Charge

0.9

0.95

1.05

1.1

Ratio

Figure 34: Charge of the ﬁrst 100 PFCs in ggH,

within_jets, varying under PS weights

2.5.3 Eta

Unlike the other variables, we observe a typical variation of order ∼ 5% both in_any_jet and not_in_any_jet

(under the weights’ variation, for ggH), with no speciﬁc behavior depending on the type of particle.

For the CP5 tune variations, we observe little ﬂuctuations for the subregion not_in_any_jet, but greater ones

(up to 30 % of the nominal) in in_any_jet. Nevertheless, there is still no clear oﬀset of shape eﬀect, and those

ﬂuctuations are likely due to few statistics.

0.02

0.04

0.06

0.08

0.1

0.12

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

4− 2− 0 2 4

0.95

1.05

Ratio

Figure 35: eta of the ﬁrst 100 PFCs in ggH,

in_any_jet, varying under PS weights

0.02

0.04

0.06

0.08

0.1

a.u.

(13.6 TeV)

CMS

Simulation

Work in progress

nominal

weight_ps_fsr_down

weight_ps_fsr_up

weight_ps_isr_down

weight_ps_isr_up

4− 2− 0 2 4

0.95

1.05

Ratio

Figure 36: eta of the ﬁrst 100 PFCs in ggH,

not_in_any_jet, varying under PS weights

3 Conclusion

During this internship, we tried to probe the feasibility of using Graph Neural Networks (GNNs) to classify vector

boson fusion from gluon-gluon fusion production modes of the Higgs boson. The study focused on quantifying the

stability of Monte Carlo simulations, analyzing the impact of variations in parton shower weights and CP5 tunes on

classiﬁcation performance.

The results show that while the DNN score ﬂuctuates within a 10-20% range under these variations, the ROC

curves remain stable within 1%. The main deviations observed come from underlying events and are particularly

visible when looking at the transverse momentum of the particle ﬂow candidates.

Future work could focus on retraining the DNN with updated particle selection criteria to verify the result of

this study and apply the same type of analysis on the CP5 tunes variations of the gluon-gluon fusion.

Acknowledgment

I’d like to thank Dr. Andrea Malara for his support throughout the internship, and above all for moving heaven and

earth to enable me to complete it in the best possible conditions.

I’d also like to thank Dr. Santeri Laurila, Prof. Pascal Vanlaer and Prof. Stephane Goriely for their help and

availability, even when the schedule was tight. Finally, I’d like to thank the CERN’s Summer Student program team

and participants for this amazing summer. Special thanks to Elio for our fascinating discussions on histograms.

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